Answer
$-\dfrac{3 \sqrt 3}{2} -\dfrac{3}{2}\ i$
Work Step by Step
We know from the unit circle that:
$\cos 210^{\circ}=-\dfrac{\sqrt 3}{2}$
$\sin 210^{\circ}=\dfrac{1}{2}$
Thus,, we simplify the given expression as follows:
$3[\cos (210^{\circ})+i \ \sin (210^{\circ})]
\\=3 (-\dfrac{\sqrt 3}{2} -i \cdot\dfrac{1}{2})
\\=3 \left(-\dfrac{\sqrt 3}{2}\right) - 3\left(i \cdot\dfrac{1}{2}\right)
\\=-\dfrac{3 \sqrt 3}{2} -\dfrac{3}{2}\ i$
